Kondo effect in XXZ spin chains

TL;DR

This paper investigates the Kondo effect in a one-dimensional XXZ spin chain with an impurity, combining analytical RG analysis and numerical DMRG methods to understand impurity screening and chain behavior across different anisotropy regimes.

Contribution

It provides a combined analytical and numerical study of the Kondo effect in XXZ chains, revealing impurity screening mechanisms and chain healing phenomena in various anisotropy regimes.

Findings

Impurity spin is screened forming a singlet with a chain spin.

In the antiferromagnetic regime, the chain is effectively cut into two.

In the ferromagnetic regime, the chain remains intact due to healing.

Abstract

The Kondo effect in a one-dimensional spin-1/2 XXZ model in the gapless XY regime (-1<Delta<=1) is studied both analytically and numerically. In our model an impurity spin (S=1/2) is coupled to a single spin in the XXZ spin chain. Perturbative renormalization-group (RG) analysis is performed for various limiting cases to deduce low-energy fixed points. It is shown that in the ground state the impurity spin is screened by forming a singlet with a spin in the host XXZ chain. In the antiferromagnetic side (0<Delta<=1) the host chain is cut into two semi-infinite chains by the singlet. In the ferromagnetic side (-1<Delta<0), on the other hand, the host XXZ chain remains as a single chain through "healing" of a weakened bond in the low-energy (long-distance) limit. The density matrix renormalization group method is used to study the size scaling of finite-size energy gaps and the power-law decay of correlation functions in the ground state. The numerical results are in good agreement with the predictions of the RG analysis. Low-temperature behaviors of specific heat and susceptibility are also discussed.